Autism Spectrum Disorder (ASD) is a heterogeneous disorder characterized by specific behavioral deficits. However, its altered developmental trajectory can also lead to cognitive strengths, particularly in the domains of mathematical and analytical problem solving. Mathematical cognition is critical not only for success in science and engineering but also as an important skill in everyday life, second only to reading. Despite its importance, numerical and mathematical reasoning is a grossly understudied cognitive domain in ASD. Here, we propose to initiate the first systematic study of mathematical cognition in children with ASD, focusing initially on children with High Functioning Autism (HFA). The overarching goal of this proposal is to investigate number sense, mathematical reasoning and problem solving abilities in children with HFA using a cognitive and systems neuroscience approach. The specific aims of this project are: (1) To behaviorally characterize mathematical abilities in children with ASD using a battery of standardized and novel cognitive tests, (2) To investigate the cognitive and brain processes underlying basic number sense in children with ASD and compare them to typically developing (TD) children, (3) To investigate the cognitive and brain processes underlying arithmetic problem solving abilities in children with ASD and compare them to TD children, and (4) To examine the integrity of functional and structural networks supporting mathematical cognition in children with ASD compared to TD children. We will test the hypotheses that (i) mathematical cognition is an islet of relative ability in some children with ASD and (ii) children with ASD, whether they exhibit superior, equivalent, or poorer performance levels as TD controls, will deploy atypical brain processes during numerical and mathematical problem solving. Our proposed studies will provide new insights into the neural basis of mathematical abilities in children with ASD, and the extent to which brain networks supporting mathematical information processing are altered in these children. If, as we predict, mathematical skills are an islet of ability in some children with ASD, the proposed studies will provide novel insights into the neurobiological mechanisms underlying cognitive and behavioral heterogeneity in children with ASD. Our research will not only lead to a more thorough understanding of the neural systems mediating heterogeneity of cognitive functioning and problem solving abilities in ASD, but it will also have important implications for designing appropriate interventions to improve academic, vocational and professional achievement in individuals with ASD by identifying their unique strengths and weaknesses at an early age.